   Chapter 6.2, Problem 48E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Given concentric circles with center O , Δ A B C is inscribed in the larger circle, as shown. If B C ¯ is tangent to the smaller circle at point T and A B = 8 , find the length of the radius of the smaller circle. To determine

To find:

The length of the radius of the smaller circle.

Explanation

Calculation:

Given, concentric circles with center O.

ΔABC is inscribed in the larger circle as shown below.

It is also given that, BC¯ is tangent to the smaller circle at point T and AB=8.

Now draw a line joining O and T.

OT is the radius of smaller circle and OA is the radius of the bigger circle.

So, OTCT.

OTC=90°.

From the figure, ABBC.

So, ABC=90°

Therefore,

OTC=ABC

And again from the figure,

OCT=ACB

Hence, ΔOTCΔABC by AA similarity

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